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Question
Assuming that x, y, z are positive real numbers, simplify the following:
`(sqrt2/sqrt3)^5(6/7)^2`
Solution
We have to simplify the following, assuming that x, y, z are positive real numbers
Given `(sqrt2/sqrt3)^5(6/7)^2`
`=(sqrt2/sqrt3)^(2+2+1)(6/7)^2`
`=(sqrt2/sqrt3)^2xx(sqrt2/sqrt3)^2xx(sqrt2/sqrt3)^1xx(6/7)^2`
`=(2/3)xx(2/3)xx(sqrt2/sqrt3)^1xx(6/7)^2`
`=(16sqrt2)/(49sqrt3)`
`=sqrt(512/7203)`
`=(512/7203)^(1/2)`
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